# Flower shape from 5 points on a polar coordinate plane

- Author:
- jupa2011

The polyline is used to draw the flower-locus. You may drag the points to reshape the flower.
Flower locus is a "u"-vector rotating around "K"-point. "u" is a instance of a "vector"-vector. Flower points are vector values, vector values from the "a"-polyline.
Polyline is a function graph. It represents a graph that is in polar coordinates, but the polar coordinates are displayed in XY-coordinate plane.
The 5 points in the "a"-polyline points are minima/maxima vector values. https://en.wikipedia.org/wiki/Maxima_and_minima
For example, point F representes a vector-value of a "vector"-vector variable, in polar coordinates: "F"-vector is a 6.77;1.09 radians
The function ("a"-polyline) maps from Angles --> (Angle,Imaginary number) ordered pairs.
Range of a function is Angles and domain of a function are (Angle, Imaginary value)-values.
Function maps from x to a vector (i,x)
This material shows that with just 5 points (points are actually values of a vector variable in polar coordinates), it is possible to draw a complex shape.
(Actually I am not sure what I am doing at this material. )
If You rearrange the points to horizontal line, you get a circle https://en.wikipedia.org/wiki/Euler's_formula#Relationship_to_trigonometry
I believe the natural number e https://en.wikipedia.org/wiki/Exponential_function is present in some way. The interesting thing here is showing the polar coordinates as XY-coordinates, and how elegantly those 5 points describe the flower. 5 points and simple interpolation!
Yes there are sine roses https://www.geogebra.org/m/P3MNkXkJ

Drag points to a single horizontal line, see how the shape changes to a circle